Conventionally, a tire component is supplied to a first conveyor, cut at a cutting system between the first roller conveyor and a second roller conveyor, and subsequently conveyed by the second roller conveyor towards a transfer drum or towards a building drum. At each transition of the tire components from one roller conveyor to the next roller conveyor, or from a roller conveyor to a drum, the tire component is momentarily unsupported, and its actual position may shift with respect to the intended or theoretical position. In particular, at the transition from a roller conveyor to a drum, the roller conveyor can not physically extend up to the circumferential surface of the drum, and the tire component is dropped over the remaining distance from the last roll of the roller conveyor onto the circumferential surface of the drum. Thus, a direct and reliable transfer of the tire component is not possible.